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This volume tackles more advanced themes often found in longer three-semester, or specialist further advanced postgraduate courses. It provides an introductory review to contemporary advanced topics in QFT, in particular, lattice field theory, topological field configurations, supersymmetry and the AdS/CFT correspondence, and it includes a systematic introduction to the functional renormalization group equation with application in noncommutative scalar field theory. Some non-perturbative methods, which allow exact solutions in lower dimensions, or due to the larger number of symmetries involved, are also discussed. This new edition also includes chapters added on noncommutative field theory and the SYK models.
Key Features:
- Reorganized, updated and extended new edition
- Four new chapters.
- Additional exercises
- Suitable for extended courses
Prologue
Author biography
12 The Wilson and functional renormalization group equations
13 Some exact solutions of quantum field theory
14 The monopoles and instantons
15 Introducing supersymmetry
16 The AdS/CFT correspondence
17 Conformal field theory and emergence of conformal symmetry
18 Novel phenomena in noncommutative field theory: emergent geometry
19 Noncommutative scalar field theory and its renormalizability
20 The neural network method for quantum field theory
Appendix A: Lie algebra representation theory: a primer A-1
Appendix B: On homotopy theory